Fractal generalized zone plates

The construction of fractal generalized zone plates from a set of periodic diffractive optical elements with circular symmetry is proposed. This allows us, for instance, to increase the number of foci of a conventional fractal zone plate while keeping the self-similarity property within the axial irradiance. The focusing properties of these fractal diffractive optical elements for points not only along but also in the close vicinity of the optical axis are investigated. In both cases analytical expressions for the irradiance are derived. Numerical simulations of the energetic efficiency of fractal generalized zone plates under plane wave illumination are carried out. In addition, some effects on the axial irradiance caused by variations in the area of their transparent rings are shown.